Poncelet theorems

Details Poncelet theorems Poncelet theorems

1995-02-16

arxiv.org/abs/alg-geom/9502017v1

Mathematics

Algebraic Geometry

20 pages, LaTeX

Scientific paper

If there is one polygon inscribed into some smooth conic and circumscribed about another one, then there are infinitely many such polygons. This is Poncelet's theorem. The aim of this note is to collect some (mostly classical) versions of this theorem, namely: - Weyr's Poncelet theorem in $P_3$ (1870), - Emch's theorem on circular series (1901), - Gerbaldi's formula for the number of Poncelet pairs (1919), - the Money-Coutts theorem on three circles (1971), - the zig-zag theorem (1974), - a (probably new) Poncelet theorem on three conics, - a Poncelet formula for quadrics of revolution.

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